NDLI: Rational points on Erdős–Selfridge superelliptic curves

Content Provider	Scilit
Author	Bennett, Michael A. Siksek, Samir
Copyright Year	2016
Description	Journal: Compositio Mathematica Given $k\geqslant 2$, we show that there are at most finitely many rational numbers $x$ and $y\neq 0$ and integers $\ell \geqslant 2$ (with $(k,\ell )\neq (2,2)$) for which $\begin{eqnarray}x(x+1)\cdots (x+k-1)=y^{\ell }.\end{eqnarray}$ In particular, if we assume that $\ell$ is prime, then all such triples $(x,y,\ell )$ satisfy either $y=0$ or $\ell <\exp (3^{k})$.
Ending Page	2254
Starting Page	2249
ISSN	00221295
e-ISSN	15705846
DOI	10.1112/s0010437x16007569
Journal	Compositio Mathematica
Issue Number	11
Volume Number	152
Language	English
Publisher	Wiley-Blackwell
Publisher Date	2016-07-14
Access Restriction	Open
Subject Keyword	Journal: Compositio Mathematica Mathematical Physics Rational Points Selfridge Superelliptic Curves
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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Rational points on Erdős–Selfridge superelliptic curves